《高等数理统计》课程教学资源（书籍文献）Mathematical Statistics with Applications，7th Edition，Dennis D. Wackerly、William Mendenhall III、Richard L. Scheaffer

WACKERLY·MENDENHALL·SCHEAFFERMathematicalStatisticswithApplications7thEdition

CONTENTSPrefacexiliNote to the Studentxxi>WhatIs Statistics?11.1Introduction11.2Characterizing a Set of Measurements: Graphical Methods31.3Characterizing a Set of Measurements:Numerical Methods81.4HowInferencesAreMade131.5Theory and Reality 141.6Summary152Probability 202.1Introduction202.2Probabilityand Inference212.3AReviewof SetNotation232.4AProbabilistic Model foranExperiment:TheDiscrete Case262.5135Calculating the Probability of an Event: The Sample-Point Method2.6ToolsforCountingSamplePoints402.7Conditional Probabilityand theIndependenceof Events512.8TwoLawsof Probability57>Copyright 2011 Cengage Les.All RightEditors

CONTENTS Preface xiii Note to the Student xxi 1 What Is Statistics? 1 1.1 Introduction 1 1.2 Characterizing a Set of Measurements: Graphical Methods 3 1.3 Characterizing a Set of Measurements: Numerical Methods 8 1.4 How Inferences Are Made 13 1.5 Theory and Reality 14 1.6 Summary 15 2 Probability 20 2.1 Introduction 20 2.2 Probability and Inference 21 2.3 A Review of Set Notation 23 2.4 A Probabilistic Model for an Experiment: The Discrete Case 26 2.5 Calculating the Probability of an Event: The Sample-Point Method 35 2.6 Tools for Counting Sample Points 40 2.7 Conditional Probability and the Independence of Events 51 2.8 Two Laws of Probability 57 v Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it

viContents2.9Calculating theProbabilityof an Event:TheEvent-CompositionMethod622.10TheLawofTotalProbabilityandBayes'Rule702.11Numerical Events and RandomVariables752.12Random Sampling772.13Summary793DiscreteRandomVariablesandTheirProbabilityDistributions863.1BasicDefinition863.2TheProbabilityDistributionforaDiscreteRandomVariable873.3TheExpected Value of a RandomVariable ora FunctionofaRandomVariable913.4TheBinomial ProbabilityDistribution1003.5The GeometricProbabilityDistribution1143.6121The Negative Binomial Probability Distribution (Optional)3.7TheHypergeometricProbabilityDistribution1253.8ThePoissonProbabilityDistribution1313.9Moments and Moment-Generating Functions1383.10Probability-GeneratingFunctions(Optional)1433.11Tchebysheff'sTheorem1463.12Summary1494 Continuous Variables and Their ProbabilityDistributions 1574.1Introduction1574.2The ProbabilityDistribution for a Continuous RandomVariable1584.3ExpectedValuesforContinuousRandomVariables1704.4TheUniformProbabilityDistribution1744.5The Normal ProbabilityDistribution1784.6The Gamma ProbabilityDistribution1854.7TheBeta ProbabilityDistribution194Copyright 2011 Ceial

vi Contents 2.9 Calculating the Probability of an Event: The Event-Composition Method 62 2.10 The Law of Total Probability and Bayes’ Rule 70 2.11 Numerical Events and Random Variables 75 2.12 Random Sampling 77 2.13 Summary 79 3 Discrete Random Variables and Their Probability Distributions 86 3.1 Basic Definition 86 3.2 The Probability Distribution for a Discrete Random Variable 87 3.3 The Expected Value of a Random Variable or a Function of a Random Variable 91 3.4 The Binomial Probability Distribution 100 3.5 The Geometric Probability Distribution 114 3.6 The Negative Binomial Probability Distribution (Optional) 121 3.7 The Hypergeometric Probability Distribution 125 3.8 The Poisson Probability Distribution 131 3.9 Moments and Moment-Generating Functions 138 3.10 Probability-Generating Functions (Optional) 143 3.11 Tchebysheff’s Theorem 146 3.12 Summary 149 4 Continuous Variables and Their Probability Distributions 157 4.1 Introduction 157 4.2 The Probability Distribution for a Continuous Random Variable 158 4.3 Expected Values for Continuous Random Variables 170 4.4 The Uniform Probability Distribution 174 4.5 The Normal Probability Distribution 178 4.6 The Gamma Probability Distribution 185 4.7 The Beta Probability Distribution 194 Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it

Contentsvii4.8SomeGeneralComments2014.9OtherExpectedValues2024.10Tchebysheff'sTheorem2074.11Expectations of Discontinuous Functions and MixedProbabilityDistributions (Optional)2104.12Summary2145MultivariateProbabilityDistributions 2235.1Introduction 2235.2224Bivariate and Multivariate ProbabilityDistributions5.3Marginal and Conditional Probability Distributions2355.4IndependentRandomVariables2475.5TheExpectedValueof aFunctionof RandomVariables2555.6SpecialTheorems2585.7TheCovarianceofTwoRandomVariables2645.8TheExpected Value and Variance of Linear FunctionsofRandomVariables2705.9TheMultinomialProbabilityDistribution2795.10TheBivariateNormalDistribution(Optional)2835.11Conditional Expectations2855.12Summary2906FunctionsofRandomVariables2966.1Introduction2966.2Finding the Probability Distribution of a FunctionofRandomVariables2976.3TheMethod of Distribution Functions2986.4TheMethod ofTransformations3106.5TheMethod of Moment-GeneratingFunctions3186.6MultivariableTransformations Using Jacobians (Optional)3256.7OrderStatistics3336.8Summary341Copyright 2011 Cengage IRialBditc

Contents vii 4.8 Some General Comments 201 4.9 Other Expected Values 202 4.10 Tchebysheff’s Theorem 207 4.11 Expectations of Discontinuous Functions and Mixed Probability Distributions (Optional) 210 4.12 Summary 214 5 Multivariate Probability Distributions 223 5.1 Introduction 223 5.2 Bivariate and Multivariate Probability Distributions 224 5.3 Marginal and Conditional Probability Distributions 235 5.4 Independent Random Variables 247 5.5 The Expected Value of a Function of Random Variables 255 5.6 Special Theorems 258 5.7 The Covariance of Two Random Variables 264 5.8 The Expected Value and Variance of Linear Functions of Random Variables 270 5.9 The Multinomial Probability Distribution 279 5.10 The Bivariate Normal Distribution (Optional) 283 5.11 Conditional Expectations 285 5.12 Summary 290 6 Functions of Random Variables 296 6.1 Introduction 296 6.2 Finding the Probability Distribution of a Function of Random Variables 297 6.3 The Method of Distribution Functions 298 6.4 The Method of Transformations 310 6.5 The Method of Moment-Generating Functions 318 6.6 Multivariable Transformations Using Jacobians (Optional) 325 6.7 Order Statistics 333 6.8 Summary 341 Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it

viliContents7SamplingDistributions andtheCentralLimitTheorem3467.1Introduction 3467.2SamplingDistributions Related to theNormalDistribution3537.3TheCentral LimitTheorem3707.4AProofof theCentral LimitTheorem(Optional)3777.5TheNormal ApproximationtotheBinomialDistribution3787.6Summary3858Estimation3908.1Introduction3908.2TheBias and Mean SquareErrorof Point Estimators3928.3SomeCommonUnbiasedPointEstimators3968.4Evaluating theGoodness ofa Point Estimator3998.5Confidence Intervals4068.6Large-Sample Confidence Intervals4118.7SelectingtheSampleSize4218.8Small-Sample ConfidenceIntervals for μ and μi-μ24258.9Confidence Intervals for24348.10Summary4379PropertiesofPoint Estimators and MethodsofEstimation4449.1Introduction4449.2Relative Efficiency4459.3Consistency4489.4Sufficiency4599.5TheRao-Blackwell Theorem and Minimum-VarianceUnbiasedEstimation4649.6TheMethodofMoments4729.7TheMethod of MaximumLikelihood14769.8Some Large-Sample Properties of Maximum-Likelihood483Estimators(Optional)9.9Summary485Copyright 2011 Cengage LRightEtitou

viii Contents 7 Sampling Distributions and the Central Limit Theorem 346 7.1 Introduction 346 7.2 Sampling Distributions Related to the Normal Distribution 353 7.3 The Central Limit Theorem 370 7.4 A Proof of the Central Limit Theorem (Optional) 377 7.5 The Normal Approximation to the Binomial Distribution 378 7.6 Summary 385 8 Estimation 390 8.1 Introduction 390 8.2 The Bias and Mean Square Error of Point Estimators 392 8.3 Some Common Unbiased Point Estimators 396 8.4 Evaluating the Goodness of a Point Estimator 399 8.5 Confidence Intervals 406 8.6 Large-Sample Confidence Intervals 411 8.7 Selecting the Sample Size 421 8.8 Small-Sample Confidence Intervals for μ and μ1 − μ2 425 8.9 Confidence Intervals for σ 2 434 8.10 Summary 437 9 Properties of Point Estimators and Methods of Estimation 444 9.1 Introduction 444 9.2 Relative Efficiency 445 9.3 Consistency 448 9.4 Sufficiency 459 9.5 The Rao–Blackwell Theorem and Minimum-Variance Unbiased Estimation 464 9.6 The Method of Moments 472 9.7 The Method of Maximum Likelihood 476 9.8 Some Large-Sample Properties of Maximum-Likelihood Estimators (Optional) 483 9.9 Summary 485 Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it

Contents ix10 Hypothesis Testing 48810.1Introduction48810.2ElementsofaStatisticalTest48910.3CommonLarge-SampleTests49610.4CalculatingType II Error Probabilities and Finding the Sample SizeforZ Tests50710.5Relationships Between Hypothesis-Testing Proceduresand Confidence Intervals51110.6Another Way to Report the Results of a Statistical Test:AttainedSignificanceLevels,orp-Values51310.7SomeCommentson theTheoryofHypothesisTesting51810.8Small-SampleHypothesisTestingforμand μi-μ252010.9Testing Hypotheses Concerning Variances53010.10PowerofTests andtheNeyman-Pearson Lemma54010.11Likelihood Ratio Tests54910.12Summary55611 LinearModelsandEstimationbyLeastSquares 56311.1Introduction56411.2Linear Statistical Models56611.3TheMethod of Least Squares56911.4Properties of the Least-Squares Estimators: SimpleLinear Regression 57711.5Inferences Concerning theParametersβ:58411.6Inferences Concerning Linear Functions of the ModelParameters:SimpleLinear Regression58911.7Predicting a Particular Value of Y by Using Simple LinearRegression59311.8Correlation59811.9Some Practical Examples 60411.10Fitting the LinearModel by Using Matrices60911.11LinearFunctions of the Model Parameters: Multiple LinearRegression 61511.12Inferences Concerning LinearFunctions of the Model Parameters:Multiple Linear Regression 616Copyright 2011 CengaRia

Contents ix 10 Hypothesis Testing 488 10.1 Introduction 488 10.2 Elements of a Statistical Test 489 10.3 Common Large-Sample Tests 496 10.4 Calculating Type II Error Probabilities and Finding the Sample Size for Z Tests 507 10.5 Relationships Between Hypothesis-Testing Procedures and Confidence Intervals 511 10.6 Another Way to Report the Results of a Statistical Test: Attained Significance Levels, or p-Values 513 10.7 Some Comments on the Theory of Hypothesis Testing 518 10.8 Small-Sample Hypothesis Testing for μ and μ1 − μ2 520 10.9 Testing Hypotheses Concerning Variances 530 10.10 Power of Tests and the Neyman–Pearson Lemma 540 10.11 Likelihood Ratio Tests 549 10.12 Summary 556 11 Linear Models and Estimation by Least Squares 563 11.1 Introduction 564 11.2 Linear Statistical Models 566 11.3 The Method of Least Squares 569 11.4 Properties of the Least-Squares Estimators: Simple Linear Regression 577 11.5 Inferences Concerning the Parameters βi 584 11.6 Inferences Concerning Linear Functions of the Model Parameters: Simple Linear Regression 589 11.7 Predicting a Particular Value of Y by Using Simple Linear Regression 593 11.8 Correlation 598 11.9 Some Practical Examples 604 11.10 Fitting the Linear Model by Using Matrices 609 11.11 Linear Functions of the Model Parameters: Multiple Linear Regression 615 11.12 Inferences Concerning Linear Functions of the Model Parameters: Multiple Linear Regression 616 Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it

xContents11.13Predicting a ParticularValueof YbyUsingMultipleRegression62211.14ATest for Ho:βg+1=βg+2 =...=βk=0 62411.15SummaryandConcludingRemarks63312 Considerations in Designing Experiments 64012.1The Elements Affecting theInformation in a Sample64012.2Designing Experiments to Increase Accuracy64112.3The Matched-Pairs Experiment64412.4Some ElementaryExperimental Designs65112.5Summary65713TheAnalysisof Variance 66113.1Introduction66113.2TheAnalysis of VarianceProcedure66213.3Comparisonof MoreThanTwoMeans:Analysis of VarianceforaOne-WayLayout66713.4An Analysis of VarianceTable for a One-WayLayout 67113.5AStatisticalModelfortheOne-WayLayout67713.6Proof of Additivityof the Sums of Squares andE(MST)for a One-Way Layout (Optional)67913.7Estimation in the One-WayLayout68113.8AStatistical Model for the Randomized BlockDesign68613.9TheAnalysisof VarianceforaRandomizedBlockDesign68813.10Estimation in the Randomized Block Design69513.11Selecting the Sample Size69613.12SimultaneousConfidenceIntervalsforMoreThanOneParameter69813.13Analysisof VarianceUsingLinearModels70113.14Summary70514 Analysis of CategoricalData 71314.1ADescription oftheExperiment71314.2The Chi-Square Test71414.3ATest of a Hypothesis Concerning Specified Cell Probabilities:AGoodness-of-Fit Test716Copyright 2011 Ceriah

x Contents 11.13 Predicting a Particular Value of Y by Using Multiple Regression 622 11.14 A Test for H0 : βg+1 = βg+2 =···= βk = 0 624 11.15 Summary and Concluding Remarks 633 12 Considerations in Designing Experiments 640 12.1 The Elements Affecting the Information in a Sample 640 12.2 Designing Experiments to Increase Accuracy 641 12.3 The Matched-Pairs Experiment 644 12.4 Some Elementary Experimental Designs 651 12.5 Summary 657 13 The Analysis of Variance 661 13.1 Introduction 661 13.2 The Analysis of Variance Procedure 662 13.3 Comparison of More Than Two Means: Analysis of Variance for a One-Way Layout 667 13.4 An Analysis of Variance Table for a One-Way Layout 671 13.5 A Statistical Model for the One-Way Layout 677 13.6 Proof of Additivity of the Sums of Squares and E(MST) for a One-Way Layout (Optional) 679 13.7 Estimation in the One-Way Layout 681 13.8 A Statistical Model for the Randomized Block Design 686 13.9 The Analysis of Variance for a Randomized Block Design 688 13.10 Estimation in the Randomized Block Design 695 13.11 Selecting the Sample Size 696 13.12 Simultaneous Confidence Intervals for More Than One Parameter 698 13.13 Analysis of Variance Using Linear Models 701 13.14 Summary 705 14 Analysis of Categorical Data 713 14.1 A Description of the Experiment 713 14.2 The Chi-Square Test 714 14.3 A Test of a Hypothesis Concerning Specified Cell Probabilities: A Goodness-of-Fit Test 716 Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it

Contentsxi14.4ContingencyTables72114.5r×cTableswithFixedRoworColumnTotals72914.6OtherApplications73414.7SummaryandConcludingRemarks73615NonparametricStatistics 74115.1Introduction74115.2AGeneral Two-Sample Shift Model74215.3The Sign Testfora Matched-Pairs Experiment74415.4TheWilcoxon Signed-Rank Testfor a Matched-Pairs Experiment75015.5UsingRanks for ComparingTwoPopulation Distributions:IndependentRandomSamples75515.6TheMann-WhitneyUTest:IndependentRandomSamples75815.7The Kruskal-Wallis Test for the One-Way Layout76515.8TheFriedmanTestforRandomizedBlockDesigns77115.9TheRuns Test:ATestfor Randomness77715.10RankCorrelationCoefficient78315.11SomeGeneral Commentson Nonparametric Statistical Tests78916 IntroductiontoBayesianMethodsforInference79616.1Introduction79616.2Bayesian Priors,Posteriors,and Estimators79716.3Bayesian Credible Intervals80816.4BayesianTests of Hypotheses81316.5SummaryandAdditional Comments816Appendix1MatricesandOtherUsefulMathematicalResults821A1.1MatricesandMatrixAlgebra821A1.2Additionof Matrices822A1.3Multiplicationofa MatrixbyaRealNumber823A1.4MatrixMultiplication823Copyright 2011 Co

Contents xi 14.4 Contingency Tables 721 14.5 r × c Tables with Fixed Row or Column Totals 729 14.6 Other Applications 734 14.7 Summary and Concluding Remarks 736 15 Nonparametric Statistics 741 15.1 Introduction 741 15.2 A General Two-Sample Shift Model 742 15.3 The Sign Test for a Matched-Pairs Experiment 744 15.4 The Wilcoxon Signed-Rank Test for a Matched-Pairs Experiment 750 15.5 Using Ranks for Comparing Two Population Distributions: Independent Random Samples 755 15.6 The Mann–Whitney U Test: Independent Random Samples 758 15.7 The Kruskal–Wallis Test for the One-Way Layout 765 15.8 The Friedman Test for Randomized Block Designs 771 15.9 The Runs Test: A Test for Randomness 777 15.10 Rank Correlation Coefficient 783 15.11 Some General Comments on Nonparametric Statistical Tests 789 16 Introduction to Bayesian Methods for Inference 796 16.1 Introduction 796 16.2 Bayesian Priors, Posteriors, and Estimators 797 16.3 Bayesian Credible Intervals 808 16.4 Bayesian Tests of Hypotheses 813 16.5 Summary and Additional Comments 816 Appendix 1 Matrices and Other Useful Mathematical Results 821 A1.1 Matrices and Matrix Algebra 821 A1.2 Addition of Matrices 822 A1.3 Multiplication of a Matrix by a Real Number 823 A1.4 Matrix Multiplication 823 Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it

xiiContentsA1.5IdentityElements825A1.6TheInverseofaMatrix827A1.7TheTransposeof a Matrix828A1.8AMatrixExpressionfora Systemof SimultaneousLinear Equations828A1.9InvertingaMatrix830A1.10Solving a System of Simultaneous Linear Equations834A1.11OtherUsefulMathematicalResults835Appendix 2CommonProbabilityDistributions,Means,Variances,andMoment-GeneratingFunctions837Table1 DiscreteDistributions 837Table2 ContinuousDistributions 838Appendix3Tables839Table1Binomial Probabilities839Table2Tableofe-x842Table3PoissonProbabilities843Table 4NormalCurveAreas848Table5PercentagePoints ofthetDistributions849Table6850Percentage Points of the×2DistributionsTable 7PercentagePoints of theFDistributions852Table8DistributionFunctionofU862Table9Critical Values of T in the Wilcoxon Matched-Pairs, Signed-RanksTest;n=5(1)50868Table10Distributionof theTotal Numberof RunsRinSamples of Size(n1,n2);P(R≤a)870Table11 Critical Valuesof Spearman'sRank CorrelationCoefficient872Table12RandomNumbers873Answers to Exercises877Index896Copyright2011.C

xii Contents A1.5 Identity Elements 825 A1.6 The Inverse of a Matrix 827 A1.7 The Transpose of a Matrix 828 A1.8 A Matrix Expression for a System of Simultaneous Linear Equations 828 A1.9 Inverting a Matrix 830 A1.10 Solving a System of Simultaneous Linear Equations 834 A1.11 Other Useful Mathematical Results 835 Appendix 2 Common Probability Distributions, Means, Variances, and Moment-Generating Functions 837 Table 1 Discrete Distributions 837 Table 2 Continuous Distributions 838 Appendix 3 Tables 839 Table 1 Binomial Probabilities 839 Table 2 Table of e −x 842 Table 3 Poisson Probabilities 843 Table 4 Normal Curve Areas 848 Table 5 Percentage Points of the t Distributions 849 Table 6 Percentage Points of the χ 2 Distributions 850 Table 7 Percentage Points of the F Distributions 852 Table 8 Distribution Function of U 862 Table 9 Critical Values of T in the Wilcoxon Matched-Pairs, Signed-Ranks Test; n = 5(1)50 868 Table 10 Distribution of the Total Number of Runs R in Samples of Size (n1, n2); P(R ≤ a) 870 Table 11 Critical Values of Spearman’s Rank Correlation Coefficient 872 Table 12 Random Numbers 873 Answers to Exercises 877 Index 896 Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it

PREFACEThe Purpose and Prerequisites of this BookMathematical Statistics with Applications was written for use with an undergraduate1-year sequence ofcourses (9quarter-or6semester-hours)on mathematical statistics.The intent of the text is to present a solid undergraduate foundation in statisticaltheory while providing an indication of the relevance and importance of the theoryin solving practical problems in the real world.We think a course of this type issuitable for most undergraduate disciplines, including mathematics, where contactwith applications may provide a refreshing and motivating experience.The onlymathematical prerequisite is a thorough knowledge of first-year college calculus-including sums of infinite series, differentiation, and single and double integration.Our ApproachTalkingwithstudents taking or having completeda beginning coursein mathematicalstatistics reveals a majorflaw in many courses.Students can takethecourse andleaveit without a clear understanding of the nature of statistics. Many see the theory as acollectionoftopics,weaklyor stronglyrelated,butfail to see that statisticsis a theoryof information with inference as its goal.Further, they may leave the course withoutan understanding ofthe importantrole played by statistics in scientific investigations.These considerations led us to develop a text that differs from others in three ways::First, the presentation of probability is preceded by a clear statement of theobjectiveofstatistics--statisticalinference-anditsroleinscientificresearch.As students proceed through the theory of probability (Chapters 2 through 7),they are reminded frequently of the role that major topics play in statisticalinference.The cumulative effect is that statistical inference is the dominatingtheme of the course..The second feature ofthe text is connectivity.Weexplain not only how majortopics play a role in statistical inference, but also how the topics are related toxiliCopyrigh 2011 Cer

PREFACE The Purpose and Prerequisites of this Book Mathematical Statistics with Applications was written for use with an undergraduate 1-year sequence of courses (9 quarter- or 6 semester-hours) on mathematical statistics. The intent of the text is to present a solid undergraduate foundation in statistical theory while providing an indication of the relevance and importance of the theory in solving practical problems in the real world. We think a course of this type is suitable for most undergraduate disciplines, including mathematics, where contact with applications may provide a refreshing and motivating experience. The only mathematical prerequisite is a thorough knowledge of first-year college calculus— including sums of infinite series, differentiation, and single and double integration. Our Approach Talking with students taking or having completed a beginning course in mathematical statistics reveals a major flaw in many courses. Students can take the course and leave it without a clear understanding of the nature of statistics. Many see the theory as a collection of topics, weakly or strongly related, but fail to see that statistics is a theory of information with inference as its goal. Further, they may leave the course without an understanding of the important role played by statistics in scientific investigations. These considerations led us to develop a text that differs from others in three ways: • First, the presentation of probability is preceded by a clear statement of the objective of statistics—statistical inference—and its role in scientific research. As students proceed through the theory of probability (Chapters 2 through 7), they are reminded frequently of the role that major topics play in statistical inference. The cumulative effect is that statistical inference is the dominating theme of the course. • The second feature of the text is connectivity. We explain not only how major topics play a role in statistical inference, but also how the topics are related to xiii Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it